Express your answer as a mixed number simplified to lowest terms. $8\dfrac{10}{15}-2\dfrac{3}{4} = {?}$
Answer: Simplify each fraction. $= {8\dfrac{2}{3}} - {2\dfrac{3}{4}}$ Find a common denominator for the fractions: $= {8\dfrac{8}{12}}-{2\dfrac{9}{12}}$ Convert ${8\dfrac{8}{12}}$ to ${7 + \dfrac{12}{12} + \dfrac{8}{12}}$ So the problem becomes: ${7\dfrac{20}{12}}-{2\dfrac{9}{12}}$ Separate the whole numbers from the fractional parts: $= {7} + {\dfrac{20}{12}} - {2} - {\dfrac{9}{12}}$ Bring the whole numbers together and the fractions together: $= {7} - {2} + {\dfrac{20}{12}} - {\dfrac{9}{12}}$ Subtract the whole numbers: $=5 + {\dfrac{20}{12}} - {\dfrac{9}{12}}$ Subtract the fractions: $= 5+\dfrac{11}{12}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{11}{12}$